Localization, 
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 symmetry breaking, and topological transitions in non-Hermitian quasicrystals

Acharya, Aruna Prasad; Chakrabarty, Aditi; Sahu, Deepak Kumar; Datta, Sanjoy

doi:10.1103/physrevb.105.014202

Cited by 24 publications

(6 citation statements)

References 40 publications

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“…One can also tailor and control other higherorder topological phases exhibiting two-dimensional corner and three-dimensional hinge states by tuning the gain and loss or the periodic driving [172,177,178]. Recently, the study of non-Hermitian quasi-crystals has become a point of theoretical and experimental interest, given the immense body of work that has been dedicated to this particular topic [179][180][181][182][183][184]. The Floquet driving protocol enriches the topological features in non-Hermitian quasi-crystals revealing unique localization transitions.…”

Section: Floquet Engineering Of Non-hermitian Topological Phasesmentioning

confidence: 99%

Non-Hermitian topological phases: principles and prospects

Banerjee

Sarkar

Dey

et al. 2023

J. Phys.: Condens. Matter

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The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models -- Hatano-Helson, non-Hermitian Su-Schrieffer-Heeger and non-Hermitian Chern insulator -- we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future.

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Section: Floquet Engineering Of Non-hermitian Topological Phasesmentioning

confidence: 99%

Non-Hermitian topological phases: principles and prospects

Banerjee

Sarkar

Dey

et al. 2023

J. Phys.: Condens. Matter

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“…Non-Hermitian physics has attracted extensive attention, as non-Hermitian Hamiltonian can be used to explore the properties of open systems, quantum systems with gain and loss, as well as various classical systems [1][2][3][4][5][6][7][8][9][10][11]. In general, the energy band structure of non-Hermitian systems is complex, except for certain systems with pseudo-Hermiticity and parity-time (PT ) symmetry [12][13][14]. Additionally, non-Hermiticity realization is mainly based on nonreciprocal hoppings and on-site gain-loss [2,15,16].…”

Section: Introductionmentioning

confidence: 99%

Multiple skin transitions in two-band non-Hermitian systems with long-range nonreciprocal hopping

Li,

Nie,

Cui

et al. 2024

New J. Phys.

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Non-Hermitian skin effect is a prominent feature in non-Hermitian physics, leading to novel topological properties and expanding the traditional energy band theories. In this paper, we investigate a two-band non-Hermitian system in which multiple skin transitions are induced by long-range nonreciprocal hopping. The spectral winding number under periodic boundary conditions reveals the localization directions of skin states. Further, we present the analytical solution of transition points by tracing the self-intersecting points on the complex plane. Interestingly, the current system exhibits the abundant non-Hermitian skin effects, including the normal, W-shaped, and bipolar localization properties, which the eigenstate distributions and the generalized Brillouin zone can clearly illustrate. We also provide a phase diagram to represent the skin transition properties of the system comprehensively. Further, we demonstrate that the multimer non-Hermitian lattices also present the anomalous skin effect and multiple transitions, which occur in the region of the bulk band touching, the same as the two-band lattice. Moreover, a feasible scheme is proposed to realize the current non-Hermitian system with long-range nonreciprocal hopping by a topoelectrical circuit. This work further supplies the content of skin transitions and may help us explore more plentiful localization features in the two-band non-Hermitian systems.

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“…Most works on the localized effect induced by the quasi-periodicity focus on the systems described by Hamiltonian. [17][18][19][20] In fact, discrete-time QW as a stroboscopic simulator of an effective Hamiltonian can be equivalent to a Floquet system, [21,22] in which both 0-energy states and π-energy states appear in the band gap. Meanwhile, mobility edges now are regarded as an energy threshold that distinguishes the local state from the extended state, [23][24][25][26][27][28][29] which was originally used in electronic systems to describe the migration properties of electrons in irregular crystalline potential fields.…”

Section: Introductionmentioning

confidence: 99%

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

Cui 崔,

Wang 王,

Li 李

2024

Chinese Phys. B

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We construct a one-dimensional quasiperiodic quantum walk to investigate the localization-delocalization transition. The inverse participation ratio and Lyapunov exponent are employed to be as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which is corresponding to the phase in coin operator of quantum walk.

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Localization, PT symmetry breaking, and topological transitions in non-Hermitian quasicrystals

Cited by 24 publications

References 40 publications

Non-Hermitian topological phases: principles and prospects

Non-Hermitian topological phases: principles and prospects

Multiple skin transitions in two-band non-Hermitian systems with long-range nonreciprocal hopping

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

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